call me anal but if i see 34% spell fail i expect the spell to fail 34% of the time.

i managed to fail 5 times in a row a 24% spell fail. that happen .. maths .. 0.1% of the time. i would be ok with that if not that i keep failing strings of 3/4 failures on 5% spell fails. with ANY class, ANY spell. i zap a rod 6 times and fail the 5% activation 5 times out of 11 tries - that is NOT 5% fail.

how exactly are spell fail rates calculated? because i'm at the point that i already know a 50% spell fail will need to be tried at least 5 times before it passes.

A .1% chance is actually pretty high. You should notice it roughly every 1000 times you make a decision--so about once a game. In any case, a 24% fail rate is not a spell you can count on during a fight. Getting ready for a fight, sure.

i managed to fail 5 times in a row a 24% spell fail. that happen .. maths .. 0.1% of the time.

Actually, it's not. .24^5 ~= .0001 is the probability that if you flip your weighted coin exactly 5 times you will get exactly 5 heads (where heads is our failed roll case). It is not the probability of flipping 5 heads in a row over the course of n > 5 flips. That analysis is far more complicated. See this page:

The exact solution (scroll down to "Jabberwocky" and see the last formulation above it) involves the difference of a pair of infinite series of a bunch of ugly binomial coefficients.

Now you can say, "But I started at zero when I tried to cast the spell, then I rolled 5 heads in a row, therefore .24^5." While this is not strictly incorrect, it is a biased observation. How many times does 1/1000 not happen in a game? This is Derakon's point. We (humans) evolved into pattern-recognizing machines because seeing patterns was good for our survival; it's easy to show that we err on the side of caution (seeing patterns where they don't actually exist). This is why you notice 5 fails in a row, but you fail to notice .76^n < .24^5 implies n >= 26 successes in a row.

if it were not that this is a spell which isn't cast in combat. i just now cast holy word 4 times (3 fails), then 4 times (3 fails). that's a 75% fail rate, and the game says 31%.

i've literally just used this spell under "test" conditions - due to the fail rate, the high mana cost, and the fact that it's only really useful when strongly wounded.

i understand the difference between an open set and a closed set. i failed consistently between 66% and 75% of the castings when the fail rate is 31%. or do you think every set i observe is an outlier?

no it's not, because we haven't drawn an infinite sequence. i.e. i have not "not taken into consideration all the time where the observed even DID NOT take place", but i ran a character from CL1 to CL47 and every time i cast high fail rate spells, it's never what's listed.
this, incidentally, applies to every character i play. yes i know what observation bias is.